1. Field of the Invention
The present invention relates to electronic apparatus having the function of displaying graphs and more particularly to a differentiation learning aiding apparatus with the function of displaying a graph, and a storage medium which contains a control program therefor.
2. Description of the Related Art
Recently, there are electronic calculating apparatus such as pocket or desk-top calculators which perform calculation utilizing a function, input a function expression per se, and display a graph of the inputted function.
When differentiation and/or calculation of a derived function are performed by such electronic calculating apparatus, it outputs a result of the calculation as a numerical value and further displays a graph of the derived function. However, it cannot display an increase-decrease table useful for displaying a graph.
Therefore, in learning, a learner must learn an increase-decrease table before understanding a graph. Thus, the learner must draw an increase-decrease table by hand for learning, which is very inefficient compared to displaying the graph.
The object of the present invention is to provide an electronic apparatus capable of displaying an increase-decrease table in the learning of differentiation.
(1) In order to solve the above mentioned problem, according to one aspect of the present invention, there is provided an electronic apparatus comprising:
function-setting means for setting a function;
first-order differentiating means for differentiating the function set by the function setting means to provide a first-derivative;
increase-decrease table data producing means for producing increase-decrease table data for displaying an increase-decrease table which contains an increase-decrease state of the function set by the function setting means, and positive and negative signs of values of the first-derivative function obtained by the first-order differentiating means, in predetermined domains; and
displaying means for displaying the increase-decrease table on the basis of the increase-decrease table data produced by the increase-decrease table data producing means.
According to this invention, the function is set by the function setting means. The set function is differentiated by the first-order differentiating means to provide a first derivative. The increase-decrease table data producing means produces the increase-decrease table data for displaying the increase-decrease table which contains the increase-decrease state of the function set by the function setting means, and the positive and negative signs of values of the first-derivative provided by the first-derivative differentiating means, in the predetermined domains. The increase-decrease table is then displayed on the displaying means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means.
(2) The apparatus may further comprise second-order differentiating means for obtaining a second derivative of the function by further differentiating the first-derivative provided by the first-derivative differentiating means. The increase-decrease table data producing means may produce the increase-decrease table data for displaying the increase-decrease table which contains in the predetermined domain the increase-decrease state of the function set by the function setting means, positive and negative signs of values of the first-derivative obtained by the first-order differentiating means, and positive and negative signs of values of the second derivative obtained by the second-order differentiating means.
According to this invention, the second-order differentiating means further differentiates the first-derivative obtained by the first-order differentiating means to provide the second-derivative. As described above, the increase-decrease table data producing means may produce increase-decrease table data for displaying the increase-decrease table which contains in a predetermined domain an increase-decrease state of the function set by the function setting means, positive and negative signs of values of the first-derivative obtained by the first-order differentiating means, and positive and negative signs of values of the second derivative obtained by the second-order differentiating means.
Therefore, since the second derivative is obtained, and the increase-decrease table containing the first and second derivatives is displayed, the learner can understand not only increases and decreases in a graph of the original function which is indicated by the positive and negative signs of values of the first derivative, but also a form of the graph of the original function upward and downward convex which is indicated by the positive and negative signs of values of the second derivative. Therefore, the learner can easily produce a precise graph with a reduced quantity of handwork, thereby achieving a high learning effect and an effective learning of the graph of the function and differentiation.
(3) According to the present invention, the apparatus may further comprises:
display controlling means for controlling the displaying means to displaying the increase-decrease table in a state where a portion of the increase-decrease table data is hidden, when the increase-decrease table is displayed by the displaying means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means,
increase-decrease table data inputting means for inputting data to the hidden data portion of the increase-decrease table displayed by the displaying means under control of the display controlling means; and
increase-decrease table data determining means for determining whether or not the data inputted by the increase-decrease table data inputting means coincides with the hidden data portion of the increase-decrease table data produced by the increase-decrease table data producing means to output a result of the determination.
According to this invention, the display controlling means controls the displaying means so as to display the increase-decrease table in the state where the portion of the increase-decrease table data is hidden, when the increase-decrease table is displayed by the displaying means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means. The increase-decrease table data inputting means inputs the data to the hidden data portion of the increase-decrease table displayed by the displaying means under control of the display controlling means. The increase-decrease table data determining means determines whether or not the data inputted by the increase-decrease table data inputting means coincides with the hidden data portion of the increase-decrease table data produced by the increase-decrease table data producing means to output a result of the determination.
Therefore, when the increase-decrease table is displayed by the displaying means, the portion of data is displayed in the hidden state. When the hidden data is inputted, the determining means determines whether the inputted data is proper or not and displays the result of the determination. Thus, the learner can efficiently learn drawing the increase-decrease table. In this case, no trouble to draw the entire increase-decrease table by hand is required to be taken to reduce the learner""s work. Moreover, when only the portion of data of the increase-decrease table is hidden, the learner can learn while viewing other displayed data, which is useful especially for elementary learning.
(4) The increase-decrease table data producing means may produce the decrease-decrease table data for displaying the increase-decrease table which represents the increase-decrease state of the function set by the function setting means, in two kinds of increase states and two kinds of decrease states in the predetermined domains, on the basis of the positive and negative signs of values of the first and second derivatives in the predetermined domains.
Therefore, when the increase-decrease table of the function is displayed, the increase-decrease state of the function is displayed in four states, that is, clockwise-curved rightward and downward states and counterclockwise-curved rightward and upward states on the basis of the positive and negative signs of values of the first and second derivatives in the predetermined domain. Therefore, the learner can easily image a precise graph efficiently. Further, since the increase-decrease table similar to that which the learner draws by hand is displayed, the learner can also learn how to draw the increase-decrease table.
(5) The apparatus may further comprise graphic data producing means for producing graphic data for displaying a graph of the function set by the function setting means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means. The displaying means may display the graph in a predetermined display form on the basis of the graphic data produced by the graphic data producing means.
Therefore, since the increase-decrease table and the graph are displayed by the displaying means when the learner learns the table, the learner can learn the relationship between the increase-decrease table of the function and the graph without any troublesome handwork to draw the graph, thereby reducing the learner""s load in the learning to enable the learner to learn even a complex function easily.
(6) The displaying means may display the increase-decrease table and the graph simultaneously on the basis of the increase-decrease table data produced by the increase-decrease table data producing means and the graphic data produced by the graphic data producing means. The apparatus may further comprise:
graph position specifying means for specifying a particular position on the graph displayed by the displaying means;
domain detecting means for detecting a domain corresponding to the position designated by the graph position designating means; and
emphatic display controlling means for controlling the displaying means to emphatically display a portion of the increase-decrease table displayed by the displaying means corresponding to the domain detected by the domain detecting means.
According to this invention, as described above, the displaying means may display the increase-decrease table and the graph simultaneously on the basis of the increase-decrease table data produced by the increase-decrease table data producing means and the graphic data produced by the graphic data producing means. The graph position designating means designates a particular position on the graph displayed by the displaying means. The domain detecting means detects the domain corresponding to the particular position specified by the graph position designating means. The emphatic display controlling means controls the displaying means to indicate the portion of the increase-decrease table displayed by the displaying means corresponding to the domain detected by the domain detecting means.
Therefore, since the increase-decrease table of the function and its graph are simultaneously displayed, the learner can easily learn them and clearly observe the relationship between the increase-decrease table of the function and its graph, which results in a high learning effect. Moreover, since a particular position on the graph is emphatically displayed, and further the emphatically displayed domain is also emphatically displayed in the increase-decrease table, the learner can easily observe the relationship between the increase-decrease table and the graph to produce a higher learning effect.
(7) According to this invention, the apparatus may further comprise:
higher-order differentiating means for obtaining a higher-order derivative by differentiating the second derivative obtained by the second-order differentiating means a required numbers of times, and for sequentially outputting the higher-order derivative obtained by the respective differentiating means; and
graphic display controlling means for controlling the displaying means to display graphs of the first derivative obtained by the first-order differentiating means, the second derivative obtained by the second-order differentiating means, and the higher-order derivatives obtained sequentially by the higher-order differentiating means.
According to this invention, the higher-order differentiating means obtains a higher-order derivative by differentiating the second derivative obtained by the second-order differentiating means a required number of times, and sequentially outputs higher-order derivatives obtained by the respective differentiating means. The graphic display controlling means controls the displaying means to display graphs of the first derivative obtained by the first-order differentiating means, the second-order derivative obtained by the second-order differentiating means, and the higher-order derivatives obtained sequentially by the higher-order differentiating means.
Therefore, since a graph of a predetermined function, its first and second derivatives are displayed, the learner can get a higher learning effect. Especially, when the learner learns a complex function, the leaner can easily learn, utilizing the graph, without drawing the graph by hand which is a large load on the learner.
(8) According to the present invention, there is provided an electronic apparatus comprising:
function setting means for setting a plurality of functions;
supposing means for setting domains for the plurality of functions set by the function setting means and for supposing the relationship in magnitude between the plurality of functions in the domain;
function producing means for producing a new function representing a difference between the plurality of functions in accordance with the relationship in magnitude between the plurality of functions supposed by the supposing means;
differentiating means for differentiating the new function produced by function producing means to provide a first derivative and for differentiating the first derivative to obtain a second derivative;
increase-decrease table data producing means for producing increase-decrease table data which displays an increase-decrease table which contains the positive and negative signs of values of the first and second derivatives in the domains set by the supposing means, and the increase-decrease state of the new function;
determining means for determining whether or not the relationship in magnitude between the plurality of functions supposed by the supposing means is correct by referring to the increase-decrease state of the new function, in the increase-decrease table data produced by the increase-decrease table data producing means, on the basis of the increase-decrease state of the new function; and
displaying means for displaying the increase-decrease table on the basis of the increase-decrease table data produced by the increase-decrease table data producing means, and for displaying a result of the determination by the determining means.
According to this invention, the function setting means sets a plurality of functions. The supposing means sets the domain of the plurality of functions set by the function setting means and supposes the relationship in magnitude between the plurality of functions in the domain. The function producing means produces a new function representing the difference between the plurality of functions. The differentiating means differentiates the new function produced by the differentiating means to obtain a first derivative, and further differentiates the first derivative to obtain a second derivative. The increase-decrease table data producing means produces increase-decrease table data for displaying the increase-decrease table which contains positive and negative signs of the values of the first and second derivatives in the domain set by the supposing means, and the increase-decrease state of the new function. The determining means determines whether or not the relationship in magnitude between of the plurality of functions supposed by the supposing means is correct by referring to the increase-decrease state of the new function in the increase-decrease table data produced by the increase-decrease table data producing means. The displaying means displays the increase-decrease table on the basis of the increase-decrease table data produced by the increase-decrease table data producing means, and displays a result of the determination by the determining means. Thus, the leaner can easily learn applied problems in the differentiating method. Especially, even when a complex function is handled, an amount of the learner""s handwork required for the learning is greatly reduced. Thus, even the complex function can be easily handled.
(9) According to the invention, there is provided an electronic apparatus, comprising;
dimension table containing means containing a dimension table in which a plurality of units of physical quantities are set in correspondence with a plurality of dimensions of the units;
physical quantity inputting means for inputting a physical quantity represented as a function of a predetermined variable and a unit of the physical quantity;
differentiating means for differentiating the function inputted as the physical quantity by the physical quantity inputting means with respect to a predetermined variable to obtain a derivative;
dimension table referencing means for obtaining the unit of a physical quantity which is represented by the derivative which is obtained by the differentiating means, by referencing the dimension table contained in the dimension table containing means on the basis of the unit of a physical quantity inputted by the physical quantity inputting means; and
displaying means for displaying the derivative obtained by the differentiating means and the unit of a physical quantity obtained by the dimension table referencing means.
According to this electronic apparatus, the dimension table containing means contains a dimension table in which a plurality of units of physical quantities are set in correspondence with a plurality of dimensions of units. The physical quantity inputting means inputs a physical quantity represented as a function of a predetermined variable and the unit of the physical quantity. The differentiating means differentiates the function inputted as the physical quantity by the physical quantity inputting means with respect to the predetermined variable to obtain a derived function. The dimension table referencing means references the dimension table contained in the dimension table containing means to obtain the unit of a physical quantity which is represented by the derived function obtained by the differentiating means, on the basis of the unit of the physical quantity inputted by the physical quantity inputting means. The displaying means displays the derivative obtained by the differentiating means and the unit obtained by the dimension table referencing means. The learner can learn application of a differentiating method in physics. A dimension is gotten by referring to the dimension table based on the unit of the input physical quantity, and a unit is gotten by referring to the dimension table based on the dimension obtained after the differentiation. Thus, even a unit of little note and remotely related to the differentiating process can be handled securely by setting it beforehand in the dimension table, and efficiently processed. Thus, the learner can learn extensively.
(10) According to another aspect of the present invention, there is also provided a storage medium which contains a computer executable program comprising:
a program code for setting a function,
a program code for differentiating the function to obtain a first-derivative;
a program code for producing increase-decrease table data to display an increase-decrease table which contains an increase-decrease state of the function, and positive and negative signs of values of the first-derivative, in predetermined domains; and
a program code for causing displaying means to display the increase-decrease table on the basis of the increase-decrease table data.
According to this invention, the first-derivative is obtained from the function set by the function setting means, and the increase-decrease table of the set function is displayed. Therefore, the learner can observe the increase-decrease table without manual calculation when a graph of the function is created in the learning of differentiation. Thus, the learner""s work in learning is reduced. The learner can easily understand the increase-decrease state of the graph, and create the graph efficiently. In contrast, in the conventional learning, the learner is likely to lose his strong will to learn the differentiation because simple wearisome calculations are required to be performed manually, thereby making it difficult to achieve the learning purpose that the learner should create the graph by understanding the increase-decrease state of the graph. According to the present invention, the learner can easily understand the increase-decrease state of the graph, thereby heightening his or her strong will to create the graph and increasing the learning effects.
(11) According to the present invention, there is provided a storage medium which contains a computer executable program comprising:
a program code for setting a plurality of functions;
a program code for setting domains of the plurality of functions and for supposing the relationship in magnitude between the plurality of functions in the domains;
a program code for producing a new function representing a difference between the plurality of functions in accordance with the supposed relationship in magnitude;
a program code for differentiating the new function to obtain a first derivative and for further differentiating the first derivative to obtain a second derivative;
a program code for producing increase-decrease table data for displaying an increase-decrease table which contains positiveness and negativeness of values of the first and second derivatives, and the increase-decrease state of the new function, in the set domains;
a program code for determining whether or not the relationship in magnitude between the plurality of functions is correct, by referencing the increase-decrease state of the new function in the increase-decrease table data; and
a program code for displaying the increase-decrease table on the basis of the increase-decrease table data, and a result of the determination by the determining means.
Therefore, when the learner learns a mathematical solution of the relationship in magnitude between plurality of functions, using a differential calculus, a function representing the difference between the plurality of functions is produced, and an increase-decrease table for the function is produced, and then the relationship in magnitude between the plurality of functions is determined on the basis of the increase-decrease table. Therefore, the learner can easily learn applied problems of the differentiation. Especially, even when a function to be handled is complex, the learner""s handwork amount is greatly reduced. Thus, the leaner can handle the function easily and learn solution of various questions.
(12) According to the present invention, there is provided a storage medium which contains a computer executable program comprising:
a program code containing a dimension table in which a plurality of units of physical quantities are set in correspondence with dimensions of the units in dimension table storing means;
a program code for inputting a physical quantity represented as a function of a predetermined variable, and the unit of the physical quantity;
a program code for differentiating the function inputted as the physical quantity with respect to the predetermined variable to obtain a derived function;
a program code for obtaining the unit of the physical quantity represented by the derived function, by referencing the dimension table contained in the dimension table containing means on the basis of the unit of the inputted physical quantity; and
a program code for controlling displaying means to display the derived function and the unit obtained by the dimension table referencing means.
Therefore, when a physical quantity is calculated, utilizing differentiation, a derived function is obtained by differentiating a function representing the physical quantity and displayed along with the unit of the physical quantity shown by the derived function. Thus, the learner can learn application of the differentiation in physics. Moreover, an appropriate dimension is obtained by referencing the dimension table on the basis of the unit of the inputted physical quantity, and further an appropriate unit is obtained by referencing the dimension table on the basis of the dimension obtained after the differentiation. Thus, even a unit of little note and related remotely to the differentiation can be handled securely, and processed efficiently by previously setting the unit in the dimension table. Thus, the learner can learn the differentiation extensively.